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The turn (symbol tr or pla) is a unit of plane angle measurement that is the angular measure subtended by a complete circle at its center. It is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) [1] or to one revolution (symbol rev or r). [2]
If 0 < p / q < 1 then the Ford circles that are tangent to C[ p / q ] are precisely the Ford circles for fractions that are neighbours of p / q in some Farey sequence. Thus C[ 2 / 5 ] is tangent to C[ 1 / 2 ], C[ 1 / 3 ], C[ 3 / 7 ], C[ 3 / 8 ], etc. Ford circles appear also in the Apollonian ...
Each circle is tangential to the base line and its neighboring circles (see also tangent lines to circles). Fractions with the same denominator have circles of the same size. In the special case when the circle method is applied to find the coefficients of a modular form of negative weight, Hans Rademacher found a modification of the contour ...
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.
In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser 's circle problem, has a solution by an inductive method. The greatest possible number of regions, rG = , giving the sequence 1, 2, 4 ...
A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...
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